a Legendre polynomial with a condition \(n\geqslant m\)  which implies that the
photon-number (\(n\) ) involved in PASTS is always no-less than the
photon-number (\(m\) ) operated on the STS, and there is no photon distribution
when \(n<m\) ). It is obvious that when \(m=0\)  corresponding to the
STS, then the PND of STS is also a Legendre distribution [1]}.
